Find α given that 5i+4j and αj−3k have the same length.

The value of α = 4√2

The length of a vector r = xi + yj + zk with x and y component and z components , x and y  and z is |r| = √(x² + y² + z²)

Let a = 5i + 4j and b = αj − 3k

So, length of a is |a| = √(5² + 4² + 0²)

= √(25 + 16)

= √41

length of b is |b| = √(0² + α² + (-3)²)

= √(α² + 9)

Since |a| = |b|

√41 = √(α² + 9)

Squaring both sides, we have

41 = α² + 9

α² = 41 - 9

α² = 32

Taking square root of both sides, we have

α = √32

α = √(16 × 2)

α = 4√2

So, the value of α = 4√2

Learn more about length of a vector here:

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x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

answer: 323 is how many she has ☃☃⛄❄

step-by-step explanation: